You will experience serious chest injuries if a car seat bel

You will experience serious chest injuries if a car seat belt exerts than 16,000-N on you during an accident. (The seat belt is what is stopping you during a collision.) To avoid injury estimate, your minimum stopping time; and your corresponding stopping distance assuming an initial speed of 16 m/s. Indicate any other assumptions you made.

Solution

Maximum force F = 16000 N

Let the mass of the car m = 1000 kg

Initial speed of the car u = 16 m/s

Final speed of the car v = 0

Impulse J = m( u - v )

               = 1000( 16-0)

               = 16000 kg m/s

We know F = J / t

from this minimum stopping time t = J /F

                                                   = 16000 /16000

                                                    = 1 s

(b). Let the stopping distance be S

From the relation v = u+at

Accleration a = (v-u) / t

                    =(0-16)/1

                    = -16 m/s ²

From the relation v ² - u ² = 2aS

Required distance S = [v ² - u ²]/2a

                              = [ 0 ² - 16 ²] /2(-16)

                              = (16/2)

                             = 8 m